We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

In this paper, we show the existence of copure injective preenvelopes over noetherian rings
and copure flat preenvelopes over commutative artinian rings. We use this to characterize …

We consider a two sided noetherian ring R such that the character modules of Gorenstein
injective left R-modules are Gorenstein flat right R-modules. We then prove that the class of …

Full article: DG-Injective Covers, #-Injective Covers Skip to Main Content Taylor and Francis
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Let $ R $ be any ring. We prove that all direct products of flat right $ R $-modules have finite
flat dimension if and only if each finitely generated left ideal of $ R $ has finite projective …

If R is left noetherian and M is a left R-module, then we can construct a complex called an
injective resolvent of M using injective precovers. Likewise, if R is left coherent and M is a …

If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …

RINGS OVER WHICH FLAT COVERS OF SIMPLE MODULES ARE PROJECTIVE Page 1
Journal of Algebra and Its Applications Vol. 11, No. 3 (2012) 1250046 (7 pages) c© World …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

We prove that the class of Gorenstein injective modules is both enveloping and covering
over a two sided noetherian ring such that the character modules of Gorenstein injective …